Geometry and Topology of Escape II: Homotopic Lobe Dynamics

We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge geometrically upon each endpoint of every escape segment. In the present paper, we use topological techniques to: (1) show that there exists a minimal required set of escape segments within the escape-time plot; (2) develop an algorithm which computes this minimal set; (3) show that the minimal set eventually displays a recursive structure governed by an ``Epistrophe Start Rule'': a new epistrophe is spawned Delta = D+1 iterates after the segment to which it converges, where D is the minimum delay time of the complex.Comment: 13 pages, 8 figures, to appear in Chaos, second of two paper

Geometry and Topology of Escape I: Epistrophes

We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape from a bounded region of the plane as a function along the line of initial conditions, forming an ``escape-time plot''. For a chaotic system, this plot is in general not a smooth function, but rather has many singularities at which the escape time is infinite; these singularities form a complicated fractal set. In this article we prove the existence of regular repeated sequences, called ``epistrophes'', which occur at all levels of resolution within the escape-time plot. (The word ``epistrophe'' comes from rhetoric and means ``a repeated ending following a variable beginning''.) The epistrophes give the escape-time plot a certain self-similarity, called ``epistrophic'' self-similarity, which need not imply either strict or asymptotic self-similarity.Comment: 15 pages, 9 figures, to appear in Chaos, first of two paper

First Steps Toward Change in Teacher Preparation for Elementary Science

Unless introductory undergraduate science classes for prospective elementary teachers actively incorporate the philosophy of inquiry-based learning called for in K-l2 science education refom little will change in elementary science education. Thus, at James Madison University, we have developed a new integrated science core curriculum called Understanding our World [1]. This course sequence was not only designed to fulfill general education science requirements. but also to focus on content areas our students will need to know as teachers. The objectives of these courses are based on the National Science Education Standards and Virginia’s Science Standards of Learning, including earth and space science, chemistry, physics, life sciences, and environmental science [2,3]. As an integrated package, this course sequence addresses basic science content, calculation skills, the philosophy and history of science, the process of how science is done, the role of science in society, and applications of computers and technology in science. Keeping in mind that students tend to teach in the same way they were taught, Understanding our World core classes embrace the concepts associated with reform in elementary math and science

Forensic Excavation of Rock Masses: A Technique to Investigate Discontinuity Persistence

True persistence of rock discontinuities (areas with insignificant tensile strength) is an important factor controlling the engineering behaviour of fractured rock masses, but is extremely difficult to quantify using current geological survey methodologies, even where there is good rock exposure. Trace length as measured in the field or using remote measurement devices is actually only broadly indicative of persistence for rock engineering practice and numerical modelling. Visible traces of discontinuities are treated as if they were open fractures within rock mass classifications, despite many such traces being non-persistent and actually retaining considerable strength. The common assumption of 100% persistence, based on trace length, is generally extremely conservative in terms of strength and stiffness, but not always so and may lead to a wrong prediction of failure mechanism or of excavatability. Assuming full persistence would give hopelessly incorrect predictions of hydraulic conductivity. A new technique termed forensic excavation of rock masses is introduced, as a procedure for directly investigating discontinuity persistence. This technique involves non-explosive excavation of rock masses by injecting an expansive chemical splitter along incipient discontinuities. On expansion, the splitter causes the incipient traces to open as true joints. Experiments are described in which near-planar rock discontinuities, through siltstone and sandstone, were opened up by injecting the splitter into holes drilled along the lines of visible traces of the discontinuities in the laboratory and in the field. Once exposed the surfaces were examined to investigate the pre-existing persistence characteristics of the incipient discontinuities. One conclusion from this study is that visible trace length of a discontinuity can be a poor indicator of true persistence (defined for a fracture area with negligible tensile strength). An observation from this series of experiments was that freshly failed surfaces through pre-existing rock bridges were relatively rough compared to sections of pre-existing weaker areas of geologically developed (though still incipient) discontinuities. Fractographic features such as hackle and rib marks were typical of the freshly broken rock bridges, whereas opened-up areas of incipient discontinuity were smoother. Schmidt hammer rebound values were generally higher for the rock bridge areas, probably reflecting their lower degree of chemical and physical weathering

Logic brightens my day: Evidence for implicit sensitivity to logical validity.

A key assumption of dual process theory is that reasoning is an explicit, effortful, deliberative process. The present study offers evidence for an implicit, possibly intuitive component of reasoning. Participants were shown sentences embedded in logically valid or invalid arguments. Participants were not asked to reason but instead rated the sentences for liking (Experiment 1) and physical brightness (Experiments 2-3). Sentences that followed logically from preceding sentences were judged to be more likable and brighter. Two other factors thought to be linked to implicit processing-sentence believability and facial expression-had similar effects on liking and brightness ratings. The authors conclude that sensitivity to logical structure was implicit, occurring potentially automatically and outside of awareness. They discuss the results within a fluency misattribution framework and make reference to the literature on discourse comprehension.10 page(s

Constraining recent lead pollution sources in the North Pacific using ice core stable lead isotopes

Trends and sources of lead (Pb) aerosol pollution in the North Pacific rim of North America from 1850 to 2001 are investigated using a high-resolution (subannual to annual) ice core record recovered from Eclipse Icefield (3017 masl; St. Elias Mountains, Canada). Beginning in the early 1940s, increasing Pb concentration at Eclipse Icefield occurs coevally with anthropogenic Pb deposition in central Greenland, suggesting that North American Pb pollution may have been in part or wholly responsible in both regions. Isotopic ratios (208Pb/207Pb and 206Pb/207Pb) from 1970 to 2001 confirm that a portion of the Pb deposited at Eclipse Icefield is anthropogenic, and that it represents a variable mixture of East Asian (Chinese and Japanese) emissions transported eastward across the Pacific Ocean and a North American component resulting from transient meridional atmospheric flow. Based on comparison with source material Pb isotope ratios, Chinese and North American coal combustion have likely been the primary sources of Eclipse Icefield Pb over the 1970–2001 time period. The Eclipse Icefield Pb isotope composition also implies that the North Pacific mid-troposphere is not directly impacted by transpolar atmospheric flow from Europe. Annually averaged Pb concentrations in the Eclipse Icefield ice core record show no long-term trend during 1970–2001; however, increasing 208Pb/207Pb and decreasing 206Pb/207Pb ratios reflect the progressive East Asian industrialization and increase in Asian pollutant outflow. The post-1970 decrease in North American Pb emissions is likely necessary to explain the Eclipse Icefield Pb concentration time series. When compared with low (lichen) and high (Mt. Logan ice core) elevation Pb data, the Eclipse ice core record suggests a gradual increase in pollutant deposition and stronger trans-Pacific Asian contribution with rising elevation in the mountains of the North Pacific rim

Anticipatory socialisation and the construction of the employable graduate: A critical analysis of employers' graduate careers websites

A discourse of employability saturates the Higher Education sector in the UK. Government and employers call on universities to produce employable graduates who are attractive to the labour market and can sustain their future marketability by taking responsibility for protean self-development. While the neoliberal assumptions behind this call have attracted robust critique, the extent to which employers shape graduating students’ subjectivities and sense of worth as (potentially employable) workers has escaped scrutiny. Inspired by Foucauldian analyses of Human Resource Management (HRM) practices, this article examines employers’ graduate careers websites and explores the discursive construction of the ‘employable graduate’. The article contends that these websites function as a mechanism of anticipatory socialisation through which HRM practices extend managerial control into the transitional space of pre-recruitment, with the aim of engaging students’ consent to particular norms of employability

Setting priorities to inform assessment of care homes’ readiness to participate in healthcare innovation: a systematic mapping review and consensus process

© 2020 The Author(s). This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly citedOrganisational context is known to impact on the successful implementation of healthcare initiatives in care homes. We undertook a systematic mapping review to examine whether researchers have considered organisational context when planning, conducting, and reporting the implementation of healthcare innovations in care homes. Review data were mapped against the Alberta Context Tool, which was designed to assess organizational context in care homes. The review included 56 papers. No studies involved a systematic assessment of organisational context prior to implementation, but many provided post hoc explanations of how organisational context affected the success or otherwise of the innovation. Factors identified to explain a lack of success included poor senior staff engagement, non-alignment with care home culture, limited staff capacity to engage, and low levels of participation from health professionals such as general practitioners (GPs). Thirty-five stakeholders participated in workshops to discuss findings and develop questions for assessing care home readiness to participate in innovations. Ten questions were developed to initiate conversations between innovators and care home staff to support research and implementation. This framework can help researchers initiate discussions about health-related innovation. This will begin to address the gap between implementation theory and practice.Peer reviewe

Between innovation and legitimation : boundaries and knowledge flow in management consultancy

Management consultancy is seen by many as a key agent in the adoption of new management ideas and practices in organizations. Two contrasting views are dominant—consultants as innovators, bringing new knowledge to their clients or as legitimating client knowledge. Those few studies which examine directly the flow of knowledge through consultancy in projects with clients favour the innovator view and highlight the important analytical and practical value of boundaries— consultants as both knowledge and organizational outsiders. Likewise, in the legitimator view, the consultants’ role is seen in terms of the primacy of the organizational boundary. By drawing on a wider social science literature on boundaries and studies of inter-organizational knowledge flow and management consultancy more generally, this polarity is seen as problematic, especially at the level of the consulting project. An alternative framework of boundary relations is developed and presented which incorporates their multiplicity, dynamism and situational specificity. This points to a greater complexity and variability in knowledge flow and its potential than is currently recognized. This is significant not only in terms of our understanding of management consultancy and inter-organizational knowledge dynamics and boundaries, but of a critical understanding of the role of management consultancy more generally